After a 50% loss in value, an investment needs a 100% return to get back to its starting value.

This is an arithmetic claim. After a 50% loss, the value is 0.5 of the original, so returning to the start needs a gain of 1/0.5 − 1 = 100%. True: the calculation confirms 100%. False: the correct required return differs from 100%. The accompanying 75% case is not part of the proposition as stated.

Set before the research began.

1. E1 Required recovery rate Exceljet · 18 January 2023

   “A 50% loss does not require a 50% gain to recover the loss, it actually requires a 100% gain.”

2. E2 Downside financial risk is misunderstood | Judgment and Decision Making | Cambridge Core Cambridge University Press (Judgment and Decision Making journal) · 4 September 2016

   “It takes a subsequent 100% return to recover from a 50% loss.”

3. E3 Common trading mistakes and the math behind them | Finabase Finabase · 30 October 2026

   “After a 50% loss, $10,000 becomes $5,000, and $5,000 has to double to get back to $10,000.”

4. E4 50 Giants: Bridgewater's Ray Dalio The Hedge Fund Journal · 1 October 2024 Own record

   “We realized we did not want to have a drawdown greater than one third, because a 50% drawdown would require a 100% return for recovery, and a 75% drawdown would require a 300% recovery.”

The claim is arithmetic: after a 50% loss, 0.5 of the original value remains, and getting back to the start takes a gain of 1/0.5 − 1 = 100%. Independent sources agree. A peer-reviewed paper says a 100% return is needed to recover from a 50% loss (E2), and Exceljet (E1) and Finabase (E3) both show the remaining value has to double. The proposition holds as stated.